Dispersion Decay for Schrödinger and Klein-Gordon Equations with a Delta-function Potential

Key Points

• This research aims to demonstrate dispersive decay in solutions to 1D Schrödinger and Klein-Gordon equations influenced by a delta-function potential.
• Proven mathematical techniques applied to 1D Schrödinger and Klein-Gordon equations.
• Focused on analyzing solutions with a delta-function potential.
• Utilized weighted norms for assessing dispersion.
• Established dispersive decay for solutions in specified weighted norms.
• Confirmed that the delta-function potential significantly impacts the decay behavior.
• Highlighted implications for understanding wave behaviors in quantum physics.